Main:i from

Average Error: 0 → 0

Time: 849.0ms

Precision: binary64

Math

\[\left(\left(\left(x + x\right) + x\right) + x\right) + x \]

↓

\[x + \left(x + \left(x + \left(x + x\right)\right)\right) \]

FPCore

(FPCore (x) :precision binary64 (+ (+ (+ (+ x x) x) x) x))

↓

(FPCore (x) :precision binary64 (+ x (+ x (+ x (+ x x)))))

C

double code(double x) {
	return (((x + x) + x) + x) + x;
}

↓

double code(double x) {
	return x + (x + (x + (x + x)));
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (((x + x) + x) + x) + x
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + (x + (x + (x + x)))
end function

Java

public static double code(double x) {
	return (((x + x) + x) + x) + x;
}

↓

public static double code(double x) {
	return x + (x + (x + (x + x)));
}

Python

def code(x):
	return (((x + x) + x) + x) + x

↓

def code(x):
	return x + (x + (x + (x + x)))

Julia

function code(x)
	return Float64(Float64(Float64(Float64(x + x) + x) + x) + x)
end

↓

function code(x)
	return Float64(x + Float64(x + Float64(x + Float64(x + x))))
end

MATLAB

function tmp = code(x)
	tmp = (((x + x) + x) + x) + x;
end

↓

function tmp = code(x)
	tmp = x + (x + (x + (x + x)));
end

Wolfram

code[x_] := N[(N[(N[(N[(x + x), $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision] + x), $MachinePrecision]

↓

code[x_] := N[(x + N[(x + N[(x + N[(x + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Error

Bits error versus x

Derivation

1. Initial program 0

   \[\left(\left(\left(x + x\right) + x\right) + x\right) + x \]

2. Final simplification 0

   \[\leadsto x + \left(x + \left(x + \left(x + x\right)\right)\right) \]

Reproduce

herbie shell --seed 2022129 
(FPCore (x)
  :name "Main:i from "
  :precision binary64
  (+ (+ (+ (+ x x) x) x) x))